How would the performance of federated learning compare to the performance of centralized machine learning when the data is i.i.d.?
There are some works that do this comparison. Briefly, it's been observed that the performance of models trained via FL drops as data distributions between participating agents differ. When data is IID-like though, performance is comparable to centralized training. Some works that I'm aware of are as follows:

Overcoming Forgetting in Federated Learning on Non-IID Data
Improving Accuracy of Federated Learning in Non-IID Settings
Federated Learning with Non-IID Data

There are probably many more around. It's an active area of research.